Question

What are the solutions of the equation x^4 + 6x^2 + 5 = 0? Use u substitution to solve.

Answer 1

Answer:

x = ±√-1 or x = ±√-5

Step-by-step explanation:

It is given an equation x^4 + 6x^2 + 5 = 0  -----(1)

Solve equation using substitution

Let y = x^2

eq (1) ⇒ y^2 + 6y + 5 =0

Solve y^2 + 6y + 5 =0

y^2 + 6y + 5 =  y^2 + 1y + 5y + 5

= y(y + 1) + 5(y + 1)

= (y + 1)(y + 5)

Therefore the zeros are -1 and -5

x^2 = -1 or x^2 = -5

x = ±√-1 or x = ±√-5

Answer 2

Answer:

x =  ±√5i or x  = ±i  is solution of given equation.

Step-by-step explanation:

We have given an equation.

x⁴+6x²+5  = 0

We to solve it using substitution.

Let u =  x²

then, u² =  x⁴

Putting above value in given equation , we have

u²+6u+5 = 0

Now, use method of factorization.

split the middle term of above equation

u²+5u+u+5 = 0

u(u+5)+1(u+5) = 0

(u+5)(u+1) = 0

Applying zero product property , we have

u+5 = 0 or u+1 = 0

u = -5 or u = -1

Putting u  = x² in above equation, we have

x² = -5 or  x² = -1

Taking square root of both sides of equations, we have

x  = ±√-5  or x = ±√-1

x =  ±√5i or x  =  ±i  where i  = √-1.